Your wage documents should be based on when you are actually paid, not when the payment was "earned." This is similar to deductions, you take them when actually paid, not when incurred or promised. (If you have a large medical expense but only pay a small part in 2015, you only deduct the amount paid, not the amount incurred.) If you are really paid on Jan 1, then those wages will be on your 2016 W-2. -- But note that if your employer writes the check and makes it available on 12/31, it will be on the 2015 W-2 even if you don't personally pick it up until after.
(That does not mean it is safe to file taxes based on your pay stub. There are a number of things that can change between your pay stub and your W-2, and if you don't get it right, you have to amend, which is a pain in the butt. But for estimating your taxes, you should figure that a check paid on Jan 1 will be on next year's W-2.)
You may wish to just ask your employer or payroll department how they intend to report it. But as Opus 17 warns above, you should never prepare a tax return on the basis of pay stubs, unless the IRS instructs you to under special circumstances when a W-2 cannot be obtained by the due date of your return. You should wait on the W-2. In fact the IRS requires that the W-2 be used.
Does this apply to direct deposit situation. The employer stated her bank cleared it on 12/31 but funds was not cleared by my bank until January 2nd. Payday is on the first but since it was holiday it wasn’t available to me or showed in my account until the 2nd. I am confused.